I'm sure it's a one of those figures of speech that has some name in Greek rhetoric, but I don't know what it is. "In the blink of an eye" means very quickly, in a fraction of a second. "Geological" is a reference to the geological time scale. They don't say exactly how long the extinction took--another source says two million years. So they are saying that when you are talking about periods of time like fifty million years, two million years was, by comparison, "in the blink of an eye." So, instead of saying "on the geologically time scale, that is like the blink of an eye," he says "in the blink of a geological eye." It isn't any standard English phrasing. The writer is being a little bit creative, colorful, or witty. Similarly, we could say "on the scale of astronomical distances, the moon is our next-door neighbor" and then shorten that to "Astronomically, the moon is our next-door neighbor."

I think what they mean is that it is a "blink of an eye" (i.e. a very short time) on a geological time scale. But the plain reading is a rather ridiculous image, isn't it?